Twisted topological structures related to M-branes II: Twisted Wu and Wu^c structures

Studying the topological aspects of M-branes in M-theory leads to various structures related to Wu classes. First we interpret Wu classes themselves as twisted classes and then define twisted notions of Wu structures. These generalize many known structures, including Pin^- structures, twisted Spin structures in the sense of Distler-Freed-Moore, Wu-twisted differential cocycles appearing in the work of Belov-Moore, as well as ones introduced by the author, such as twisted Membrane and twisted String^c structures. In addition, we introduce Wu^c structures, which generalize Pin^c structures, as well as their twisted versions. We show how these structures generalize and encode the usual structures defined via Stiefel-Whitney classes.Comment: 20 page

Chemical and Dynamical Impacts of Stratospheric Sudden Warmings on Arctic Ozone Variability

We use the Global Modeling Initiative (GMI) chemistry and transport model with Modern-Era Retrospective Analysis for Research and Applications (MERRA) meteorological fields to quantify heterogeneous chemical ozone loss in Arctic winters 2005-2015. Comparisons to Aura Microwave Limb Sounder N2O and O3 observations show the GMI simulation credibly represents the transport processes and net heterogeneous chemical loss necessary to simulate Arctic ozone. We find that the maximum seasonal ozone depletion varies linearly with the number of cold days and with wave driving (eddy heat flux) calculated from MERRA fields. We use this relationship and MERRA temperatures to estimate seasonal ozone loss from 1993 to 2004 when inorganic chlorine levels were in the same range as during the Aura period. Using these loss estimates and the observed March mean 63-90N column O3, we quantify the sensitivity of the ozone dynamical resupply to wave driving, separating it from the sensitivity of ozone depletion to wave driving. The results show that about 2/3 of the deviation of the observed March Arctic O3 from an assumed climatological mean is due to variations in O3 resupply and 13 is due to depletion. Winters with a stratospheric sudden warming (SSW) before mid-February have about 1/3 the depletion of winters without one and export less depletion to the midlatitudes. However, a larger effect on the spring midlatitude ozone comes from dynamical differences between warm and cold Arctic winters, which can mask or add to the impact of exported depletion

Gauge theory of Faddeev-Skyrme functionals

We study geometric variational problems for a class of nonlinear sigma-models in quantum field theory. Mathematically, one needs to minimize an energy functional on homotopy classes of maps from closed 3-manifolds into compact homogeneous spaces G/H. The minimizers are known as Hopfions and exhibit localized knot-like structure. Our main results include proving existence of Hopfions as finite energy Sobolev maps in each (generalized) homotopy class when the target space is a symmetric space. For more general spaces we obtain a weaker result on existence of minimizers in each 2-homotopy class. Our approach is based on representing maps into G/H by equivalence classes of flat connections. The equivalence is given by gauge symmetry on pullbacks of G-->G/H bundles. We work out a gauge calculus for connections under this symmetry, and use it to eliminate non-compactness from the minimization problem by fixing the gauge.Comment: 34 pages, no figure

GMI-IPS: Python Processing Software for Aircraft Campaigns

NASA's Atmospheric Tomography Mission (ATom) seeks to understand the impact of anthropogenic air pollution on gases in the Earth's atmosphere. Four flight campaigns are being deployed on a seasonal basis to establish a continuous global-scale data set intended to improve the representation of chemically reactive gases in global atmospheric chemistry models. The Global Modeling Initiative (GMI), is creating chemical transport simulations on a global scale for each of the ATom flight campaigns. To meet the computational demands required to translate the GMI simulation data to grids associated with the flights from the ATom campaigns, the GMI ICARTT Processing Software (GMI-IPS) has been developed and is providing key functionality for data processing and analysis in this ongoing effort. The GMI-IPS is written in Python and provides computational kernels for data interpolation and visualization tasks on GMI simulation data. A key feature of the GMI-IPS, is its ability to read ICARTT files, a text-based file format for airborne instrument data, and extract the required flight information that defines regional and temporal grid parameters associated with an ATom flight. Perhaps most importantly, the GMI-IPS creates ICARTT files containing GMI simulated data, which are used in collaboration with ATom instrument teams and other modeling groups. The initial main task of the GMI-IPS is to interpolate GMI model data to the finer temporal resolution (1-10 seconds) of a given flight. The model data includes basic fields such as temperature and pressure, but the main focus of this effort is to provide species concentrations of chemical gases for ATom flights. The software, which uses parallel computation techniques for data intensive tasks, linearly interpolates each of the model fields to the time resolution of the flight. The temporally interpolated data is then saved to disk, and is used to create additional derived quantities. In order to translate the GMI model data to the spatial grid of the flight path as defined by the pressure, latitude, and longitude points at each flight time record, a weighted average is then calculated from the nearest neighbors in two dimensions (latitude, longitude). Using SciPya's Regular Grid Interpolator, interpolation functions are generated for the GMI model grid and the calculated weighted averages. The flight path points are then extracted from the ATom ICARTT instrument file, and are sent to the multi-dimensional interpolating functions to generate GMI field quantities along the spatial path of the flight. The interpolated field quantities are then written to a ICARTT data file, which is stored for further manipulation. The GMI-IPS is aware of a generic ATom ICARTT header format, containing basic information for all flight campaigns. The GMI-IPS includes logic to edit metadata for the derived field quantities, as well as modify the generic header data such as processing dates and associated instrument files. The ICARTT interpolated data is then appended to the modified header data, and the ICARTT processing is complete for the given flight and ready for collaboration. The output ICARTT data adheres to the ICARTT file format standards V1.1. The visualization component of the GMI-IPS uses Matplotlib extensively and has several functions ranging in complexity. First, it creates a model background curtain for the flight (time versus model eta levels) with the interpolated flight data superimposed on the curtain. Secondly, it creates a time-series plot of the interpolated flight data. Lastly, the visualization component creates averaged 2D model slices (longitude versus latitude) with overlaid flight track circles at key pressure levels. The GMI-IPS consists of a handful of classes and supporting functionality that have been generalized to be compatible with any ICARTT file that adheres to the base class definition. The base class represents a generic ICARTT entry, only defining a single time entry and 3D spatial positioning parameters. Other classes inherit from this base class; several classes for input ICARTT instrument files, which contain the necessary flight positioning information as a basis for data processing, as well as other classes for output ICARTT files, which contain the interpolated model data. Utility classes provide functionality for routine procedures such as: comparing field names among ICARTT files, reading ICARTT entries from a data file and storing them in data structures, and returning a reduced spatial grid based on a collection of ICARTT entries. Although the GMI-IPS is compatible with GMI model data, it can be adapted with reasonable effort for any simulation that creates Hierarchical Data Format (HDF) files. The same can be said of its adaptability to ICARTT files outside of the context of the ATom mission. The GMI-IPS contains just under 30,000 lines of code, eight classes, and a dozen drivers and utility programs. It is maintained with GIT source code management and has been used to deliver processed GMI model data for the ATom campaigns that have taken place to date

Model study of the cross-tropopause transport of biomass burning pollution

We present a modeling study of the troposphere-to-stratosphere transport (TST) of pollution from major biomass burning regions to the tropical upper troposphere and lower stratosphere (UT/LS). TST occurs predominately through 1) slow ascent in the tropical tropopause layer (TTL) to the LS and 2) quasi-horizontal exchange to the lowermost stratosphere (LMS). We show that biomass burning pollution regularly and significantly impacts the composition of the TTL, LS, and LMS. Carbon monoxide (CO) in the LS in our simulation and data from the Aura Microwave Limb Sounder (MLS) shows an annual oscillation in its composition that results from the interaction of an annual oscillation in slow ascent from the TTL to the LS and seasonal variations in sources, including a semi-annual oscillation in CO from biomass burning. The impacts of CO sources that peak when ascent is seasonally low are damped (e.g. Southern Hemisphere biomass burning) and vice-versa for sources that peak when ascent is seasonally high (e.g. extra-tropical fossil fuels). Interannual variation of CO in the UT/LS is caused primarily by year-to-year variations in biomass burning and the locations of deep convection. During our study period, 1994–1998, we find that the highest concentrations of CO in the UT/LS occurred during the strong 1997–1998 El Niño event for two reasons: i. tropical deep convection shifted to the eastern Pacific Ocean, closer to South American and African CO sources, and ii. emissions from Indonesian biomass burning were higher. This extreme event can be seen as an upper bound on the impact of biomass burning pollution on the UT/LS. We estimate that the 1997 Indonesian wildfires increased CO in the entire TTL and tropical LS (>60 mb) by more than 40% and 10%, respectively, for several months. Zonal mean ozone increased and the hydroxyl radical decreased by as much as 20%, increasing the lifetimes and, subsequently TST, of trace gases. Our results indicate that the impact of biomass burning pollution on the UT/LS is likely greatest during an El Niño event due to favorable dynamics and historically higher burning rates

Objective analysis of tidal fields in the Atlantic and Indian Oceans

An objective analysis technique has been developed to extrapolate tidal amplitudes and phases over entire ocean basins using existing gauge data and the altimetric measurements which are now beginning to be provided by satellite oceanography. The technique was previously tested in the Lake Superior basin. The method has now been developed and applied in the Atlantic-Indian ocean basins using a 6 deg x 6 deg grid to test its essential features. The functions used in the interpolation are the eigenfunctions of the velocity potential (Proudman functions) which are computed numerically from a knowledge of the basin's bottom topography, the horizontal plan form and the necessary boundary conditions. These functions are characteristic of the particular basin. The gravitational normal modes of the basin are computed as part of the investigation, they are used to obtain the theoretical forced solutions for the tidal constituents, the latter provide the simulated data for the testing of the method and serve as a guide in choosing the most energetic modes for the objective analysis. The results of the objective analysis of the M2 and K1 tidal constituents indicate the possibility of recovering the tidal signal with a degree of accuracy well within the error bounds of present day satellite techniques

Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators

The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal connection of a Stiefel U(N)-bundle over a Grassmann manifold. Most significantly, for an arbitrary initial state, this geometric phase captures the inherent geometric feature of the state evolution. Moreover, the geometric phase in the evolution of the eigenspace of an adiabatic action operator is also addressed, which is elaborated by a pullback U(N)-bundle. Several intriguing physical examples are illustrated.Comment: Added Refs. and corrected typos; 4 page

Some Remarks on Group Bundles and C*-dynamical systems

We introduce the notion of fibred action of a group bundle on a C(X)-algebra. By using such a notion, a characterization in terms of induced C*-bundles is given for C*-dynamical systems such that the relative commutant of the fixed-point algebra is minimal (i.e., it is generated by the centre of the given C*-algebra and the centre of the fixed-point algebra). A class of examples in the setting of the Cuntz algebra is given, and connections with superselection structures with nontrivial centre are discussed.Comment: 22 pages; to appear on Comm. Math. Phy

Generalised G2G_2-manifolds

We define new Riemannian structures on 7-manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class. The unconstrained critical points generalise the notion of a manifold of holonomy $G_2$, while the constrained ones give rise to a new geometry without a classical counterpart. We characterise these structures by the means of spinors and show the integrability conditions to be equivalent to the supersymmetry equations on spinors in supergravity theory of type IIA/B with bosonic background fields. In particular, this geometry can be described by two linear metric connections with skew torsion. Finally, we construct explicit examples by using the device of T-duality.Comment: 27 pages. v2: references added. v3: wrong argument (Theorem 3.3) and example (Section 4.1) removed, further examples added, notation simplified, all comments appreciated. v4:computation of Ricci tensor corrected, various minor changes, final version of the paper to appear in Comm. Math. Phy

Baryons in Holographic QCD

We study the baryon in holographic QCD with $D4/D8/\bar{D8}$ multi-$D$ brane system. In holographic QCD, the baryon appears as a topologically non-trivial chiral soliton in a four-dimensional effective theory of mesons. We call this topological soliton as Brane-induced Skyrmion. Some review of $D4/D8/\bar{D8}$ holographic QCD is presented from the viewpoints of recent hadron physics and phenomenologies. Four-dimensional effective theory with pions and $\rho$ mesons is uniquely derived from the non-abelian Dirac-Born-Infeld (DBI) action of $D8$ brane with $D4$ supergravity background, without small amplitude expansion of meson fields to discuss chiral solitons. For the hedgehog configuration of pion and $\rho$-meson fields, we derive the energy functional and the Euler-Lagrange equation of Brane-induced Skyrmion from the meson effective action induced by holographic QCD. Performing the numerical calculation, we obtain the pion profile $F(r)$ and the $\rho$-meson profile $G(r)$ of the Brane-induced Skyrmion, and estimate its total energy, energy density distribution, and root-mean-square radius. These results are compared with the experimental quantities of baryons and also with the profiles of standard Skyrmion without $\rho$ mesons. We analyze interaction terms of pions and $\rho$ mesons in Brane-induced Skyrmion, and consider the role of $\rho$-meson component appearing in baryons.Comment: 28 pages, 11 figure